# Illustration - Problem

A factory was budgeted to produce 2,000 units of output @ one unit per 10 hours productive time working for 25 days. 40,000 for variable overhead cost and 80,000 for fixed overhead cost were budgeted to be incurred during that period.

The factory worked for 26 days putting in 860 hours work every day and achieved an output of 2,050 units. The expenditure incurred as overheads was 49,200 towards variable overheads and 86,100 towards fixed overheads.

Working Table
Standard Actual Absorbed
Budgeted for AO for AI for AP
A B C
a) Output (units)
b) Days
c) Time (hrs)
1) Variable
2) Fixed
3) Total
2,000
25

40,000
80,000
1,20,000
2,050
26

49,200
86,100
1,35,300

The working table is populated with the information that can be obtained as it is from the problem data. The rest of the information that is present in a full fledged working table that we make use of in problem solving is filled below.

# Formulae - Variable Overhead Expenditure Variance ~ VOHEXPV

Is the actual variable overhead cost incurred different from the standard cost for actual input?

The Variable Overhead Expenditure Variance is the difference between the standard variable overhead cost for actual input and the actual variable overhead incurred.

⇒ Variable Overhead Expenditure Variance (VOHEXPV)

 = SC(AI) − AC Standard Cost for actual input − Actual Cost

## Standard Cost for Actual Input (Variable Overhead)

Standard Cost for Actual Input ~ SC(AI)

= BC ×
 AI BI
Or = AI × BR/UI
Or = SO(AI) × BR/UO
Or = SP(AI) × BR/UP

Actual cost incurred is ascertained from the financial information.

Where the actual variable overhead cost incurred is not known, it can be calculated based on actual measure of the factor used for absorbing overheads like output, time worked etc. provided the related actual rate of overhead incurred is also known.

Actual Cost ~ AC

 = AO × AR/UO Or = AI × AR/UI Or = AP × AR/UP

## Formula in useful forms

 VOHEXPV = SC(AI) − AC Standard Cost for Actual Input − Actual Cost Or = AI × (BR/UI − AR/UI) Actual Input × Difference between Budgeted and Actual Rates per unit input

## Note

• Theoretically there are many possibilities. Only those that provide peculiar routes to solve problems are given as an academic exercise.
• Finding the costs by building up the working table and using the formula involving costs is the simplest way to find the VOHEFFV.

## Taking time for input and days for periods

 VOHEXPV = SC(AT) − AC Or = AT × [BR/UT − AR/UT]

# Solution - Working Notes

Standard Actual Absorbed
Budgeted for AO for AI for AP
A B C
I) Factor 1.118
a) Output (units)
b) Periods (Days)
c) Time (hrs)
1) Variable
2) Fixed
3) Total
1) Variable
2) Fixed
3) Total
(d1) ÷ (a)
(d2) ÷ (a)
(d3) ÷ (a)
1) Variable
2) Fixed
3) Total
(d1) ÷ (c)
(d2) ÷ (c)
(d3) ÷ (c)
1) Variable
2) Fixed
3) Total
(d1) ÷ (b)
(d2) ÷ (b)
(d3) ÷ (b)
2,000
25
20,000

40,000
80,000
1,20,000

2

44,720

2,050
26
22,360

49,200
86,100
1,35,300

2.2

The actual rate per hour shown as 2.2 is an approximation of
 1,230 559

One unit per 10 hours productive time

⇒ Budgeted Time per unit = 10 hours

Total Budgeted Time

 = Budgeted Output × Budgeted Time/unit = 2,000 units × 10 hrs/unit = 20,000 hrs

Total Actual Time

 = Number of Days × Actual Time/day = 26 days × 860 hrs/day = 22,360 labor/labour hrs

The following calculations are given here to give an idea. They can be made directly in the working table thus eliminating these workings.

Factor = Actual Data ÷ Standard/Budgeted Data

Relevant value = Standard/Budgeted Data × Factor

(AI) = (AT)
=
 AT BT
=
 22,360 hrs 20,000 hrs
= 1.118
SC(AI) = SC(AT)
= BC ×
 AT BT
= BC × 1.118
 SC(AT)(V) = BC(V) × 1.118 = 40,000 × 1.118 = 44,720

# Solution - (in all cases)

Since the formula for this variance does not involve absorbed overhead, the basis of absorption of overhead is not a factor to be considered in finding this variance.

 VOHEXPV = SC(AT) − AC = 44,720 − 49,200 = − 4,480 [Adv]

## Alternatives

VOHEXPV = AT × (BR/UT − AR/UT)
= 22,360 hrs × (2/hr −  1,230 559
/hr)
= 22,360 hrs × ( 1,118 − 1,230 559
/hr)
= 40 × (− 112)
= − 4,480

# Variable Overhead Expenditure Variance - Miscellaneous Aspects

• ## Nature of Variance

Based on the relations derived from the formulae for calculating VOHEXPV, we can identify the nature of Variance

• SC(AI) ___ AC
• BR/UI ___ AR/UI

The variance would be

• zero when =
• Positive when >
• Negative when <
• ## Interpretation of the Variance

The following interpretations may be made

### No Variance

The variable overhead cost incurred is as per the standard for the inputs used.

### Favourable/Favorable

The variable overhead cost incurred is lesser than the standard cost for the inputs used by the amount of the variance.

The variable overhead cost incurred is greater than the standard cost for the inputs used by the amount of the variance.
• ## Who is answerable for the Variance?

This variance is similar to material price variance and labour rate of pay variance. It reveals the variation in total cost on account of a higher rate of expenditure incurrence per unit output.

Those who are responsible for authorising expenditure incurrence are answerable for this variance.

# Formulae using Inter-relationships among Variances

1. VOHEXPV = VOHCV − VOHEFFV

## Verification

The interrelationships between variances would also be useful in verifying whether our calculations are correct or not.

Since the calculation of variable overhead expenditure variance is not influenced by the method of absorption used, the value of the variance would be the same in all cases.

Basis of Absorption
Output Input
(Time)
Periods
(Days)
VOHABSV
+ VOHEFFV
+ VOHEXPV
0
− 3,720
− 4,480
+ 3,720
− 3,720
− 4,480
+ 600
− 3,720
− 4,480
a) VOHCV − 8,200 − 4,480 − 7,600
FOHCALV
+ FOHCAPV
+ FOHEFV

FOHVOLV
FOHEXPV

b) FOHCV
TOHCV (a) + (b) − 12,300 − 1,140 − 10,500

To enable understanding we have worked out the illustration under the three possible scenarios of overhead being absorbed on output, input and period basis.

Please be aware that only one of these methods would be in use.